Syllabus

Maths has a wide range of topics from which questions are selected for each
version of NSET.

1. Number Theory
2. Exponentials and Logarithms
3. Probability and Statistics
4. Permutation and Combinations
5. Ratio and Proportion
6. Sets (Venn Diagrams)
7. Sequence and Series
8. Miscellaneous
Number theory
1. How many numbers with distinct digits are possible product of whose digits is
28?
2. A 4-digit number of the form aabb is a perfect square. What is the value of a -
b?
3. A four-digit number is formed by using only the digits 1, 2 and 3 such that both
2 and 3 appear at least once. The number of all such four-digit numbers is
4. For a 4-digit number, the sum of its digits in the thousands, hundreds and
tens places is 14, the sum of its digits in the hundreds, tens and units places is
15, and the tens place digit is 4 more than the units place digit. Then the
highest possible 4-digit number satisfying the above conditions is
5. How many two-digit numbers, with a non-zero digit in the units place, are
there which are more than thrice the number formed by interchanging the
positions of its digits?
6. A shop sells bags in three sizes: small, medium and large. A large bag costs
Rs.1000, a medium bag costs Rs.200, and a small bag costs Rs.50. Three
buyers, Ashish, Banti and Chintu, independently buy some numbers of these
types of bags. The respective amounts spent by Ashish, Banti and Chintu are
equal. Put together, the shop sells 1 large bag, 15 small bags and some
medium bags to these three buyers. What is the minimum number of
medium bags that the shop sells to them?
7. If * = +, / = -, + = *, - = / then 43 * 561 + 500 - 100 / 10 = ?
8. How many factors of 1080 are perfect squares?
9. How many numbers are there less than 100 that cannot be written as a
multiple of a perfect square greater than 1?
10. Two numbers a and b are inversely proportional to each other. If a increases by
100%, then b decreases by____?

Answer Key
1 2 3 4 5 6 7 8 9 10

8 3 50 4195 6 7 2838 4 61 50%

Exponentials and Logarithms

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Answer Key
1 2 3 4 5 6 7 8 9 10

48 7 10 47 5 36 8.25 1.5 2.25 2.285

Probability and Statistics

1. Imagine you are organizing a sports event, and you need to create a sequence
of activities. The activities can only be scheduled at times that are multiples of
4 or 6 minutes. You start listing these times in increasing order (4, 6, 8, 12, 16, 18,
20, ....). Can you determine the position of the 2024th minute in this sequence?

2. Twenty-seven athletes are randomly divided into three heats of nine for a
100m sprint. Given that Alfred is in a different heat from Richardson, and
Richardson is in a different heat from Jefferson, what is the probability that
Alfred and Jefferson are in the same heat?

3. At a carnival, there's a unique coin that is three times more likely to land on
heads compared to tails. If this coin is tossed twice, what is the probability that
exactly one of the tosses results in heads?

4. In the exciting world of football, 70% of fans support Lionel Messi, while 60%
support Cristiano Ronaldo. It is known that 40% of Messi fans also support
Ronaldo. If a randomly selected fan is known to support Ronaldo, what is the
probability that this fan also supports Messi?

5. In a magical garden, there are two ponds: Pond X and Pond Y. Pond X is filled
with 5 yellow and 2 green lilies, while Pond Y holds 2 yellow and 6 green lilies.
A magical coin is tossed to decide from which pond a flower will be picked. If
the coin lands heads, a lily is drawn from Pond X; if tails, from Pond Y. What is
the probability that the drawn lily is from Pond X, given that it is green?

6. In a magical town where every odd number between 1 and 25 represents a

unique gem, the town's gem collector needs to select 5 gems for a special
exhibition. The collector wants to ensure that the probability of choosing a
gem that has a special magical property (a prime number) from the selected
ones is 2 / 5. Can you find out how many different ways the collector can
choose these 5 gems to meet this requirement?

7. In the IPL auction, a cricket team is evaluating the acquisition of two

prominent players: Rohit and Virat. The probability that the team successfully
buys Rohit is 50%, while there is a 40% chance they will secure Virat.
Furthermore, there is a 30% probability that the team will manage to buy both
Rohit and Virat. Given this scenario, what is the probability that the team will
end up not buying either player?
8. In Shark Tank, there are 5 sharks and 5 entrepreneurs pitching their ideas.
Each shark decides to invest in an idea independently with a probability of 0.5.
What is the probability that exactly 3 entrepreneurs receive an investment?

9. In a large corporate office, each employee receives a unique entry code

assigned to activate only on a specific day of the year, with a total of 365
possible activation days available—mirroring the number of days in a non-leap
year. Given a scenario where n employees are gathered in a conference room,
determine the minimum number of employees, n, required such that the
probability of no two employees sharing the same entry code activation day is
less than 50%.

10. In the vibrant town of Autoville, 70% of the residents drive a car, and 60% ride a
bike. Interestingly, 40% of the car owners also own a bike. If you randomly
meet someone who rides a bike, what is the probability that they also drive a
car?

Answer Key
1 2 3 4 5 6 7 8 9 10

675 0.471 0.375 0.467 0.276 280 0.4 0.312 23 0.467

Permutation and Combinations

1. In a movie club, there are 4 thriller movies and 5 sci-fi movies in Collection A,
and 5 thriller movies and 4 sci-fi movies in Collection B. If 4 movies are to be
selected from each collection, how many ways are there to select 4 thriller
movies and 4 sci-fi movies?

2. You are tasked with designing a security lock system that generates 4-digit
combinations using the digits 1, 2, 3, 5, 6, and 7. The lock requires that each
digit in an even position (2nd and 4th) must be a multiple of the digit just
before it in an odd position (1st and 3rd). For instance, the combination 6342 is
valid because 6 is a multiple of 3 and 4 is a multiple of 2. How many such
4-digit combinations can you create?

3. In a futuristic digital realm where numbers are revered for their orderly
appearance, awesome numbers stand out. For example, the number 1557 is
considered awesome because its digits (1, 5, 5, and 7) are arranged in
non-decreasing order from left to right. Calculate how many awesome
numbers exist within the range [99, 9999].

4. In a tech store, there are 9 different gadgets and 8 available display racks. How
many distinct ways can the gadgets be arranged on the racks, ensuring that
each rack holds at least one gadget and all 9 gadgets are used?

5. In a university’s combinatorics class, Professor Smith posed a challenge to the

students: “Given the word 'PROBABILITY,' calculate how many arrangements
can be made after choosing any 4 letters from it."

6. In a secure online voting system, each voter is assigned a unique 3-digit

identification code to access the ballot. Each digit of the code ranges from 0 to
9. To enhance security, the system requires that each identification code
contains at least one even digit and cannot begin with the digit 0. How many
valid identification codes can be generated under these conditions?

7. A project manager has a budget of $20,000 to allocate across four different

project initiatives, each requiring funding in multiples of $1,000. Determine
how many distinct ways the total budget can be completely utilized across
these initiatives, ensuring that every dollar is allocated.
8. You are designing a secret code for a treasure hunt. The code must be a
4-digit number where the smallest digit is 3 and the largest digit is 7. How
many possible codes can you create under these conditions?

9. In preparation for the Cricket World Cup, a special promotional campaign has
been launched. A good number has been chosen to represent each team's
unique code. These good numbers must meet two conditions:
● The last two digits of the number must be divisible by 25.
● The first two digits of the number must form a prime number.

How many such good numbers exist within the range of 100,00 to 999,99
ready to be assigned to the teams?

10. In a technology convention held in San Francisco, there were only two
international exhibitors among all the attendees. Each attendee engaged in
two networking sessions with every other attendee. The number of sessions
held exclusively among the local exhibitors exceeded the number of sessions
held between local and international exhibitors by 66. How many attendees
were there at the convention?

Answer Key
1 2 3 4 5 6 7 8 9 10

5626 169 661 2902080 3702 775 1771 194 840 13

Ratio and Proportion
1. The ratio of a two-digit natural number to a number formed by reversing its
digits is 4 : 7. Which of the following is the sum of all the numbers of all such
pairs?
2. Janta Airline has a free luggage allowance for its passengers. If any passenger
carries excess luggage, it is charged at a constant rate per kg. The total
luggage charge paid by Ravind Jekriwal and Pranas Shubhan is Rs. 1100. If
both Ravind and Pranas had carried luggage twice the weight than they
actually did, their luggage charges would have been Rs. 2000 and Rs. 1000
respectively. What was the charge levied on Ravind’s luggage?
3. Class A has boys to girls in the ratio 2 : 3, Class B has girls to boys in the ratio 5 :
3. If the number of students in Class A is at least twice as many as the number
of students in Class B, what is the minimum percentage of boys when both
classes are considered together?
4. In class A, the ratio of boys to girls is 2 : 3. In class B the ratio of boys to girls is 4
: 5. If the ratio of boys to girls in both classes put together is 3 : 4, what is the
ratio of number of girls in class A to number of girls in class B?
5. A man buys juice at Rs 10/litre and dilutes it with water. He sells the mixtures
at the cost price and thus gains 11.11%. Find the quantity of water mixed by him
in every litre of juice.
6. Anil mixes cocoa with sugar in the ratio 3 : 2 to prepare mixture A, and coffee
with sugar in the ratio 7 : 3 to prepare mixture B. He combines mixtures A and
B in the ratio 2 : 3 to make a new mixture C. If he mixes C with an equal
amount of milk to make a drink, then the percentage of sugar in this drink will
be?
7. The number of coins collected per week by two coin-collectors A and B are in
the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a
multiple of 7, and the total number of coins collected by B in 3 weeks is a
multiple of 24, then the minimum possible number of coins collected by A in
one week is
8. Pinky is standing in a queue at a ticket counter. Suppose the ratio of the
number of persons standing ahead of Pinky to the number of persons
standing behind her in the queue is 3 : 5. If the total number of persons in the
queue is less than 300, then the maximum possible number of persons
standing ahead of Pinky is
9. A tea shop offers tea in cups of three different sizes. The product of the prices,
in INR, of three different sizes is equal to 800. The prices of the smallest size
and the medium size are in the ratio 2 : 5. If the shop owner decides to
increase the prices of the smallest and the medium ones by INR 6 keeping the
price of the largest size unchanged, the product then changes to 3200. The
sum of the original prices of three different sizes, in INR, is
 10. A sum of money is split among Amal, Sunil and Mita so that the ratio of the
shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is
4:5. If the difference between the largest and the smallest of these three
shares is Rs 400, then Sunil’s share, in rupees, is

Answer Key
1 2 3 4 5 6 7 8 9 10

330 800 39.17 3/5 0.111 17 42 111 34 800

Sets (Venn Diagrams)
Set A-
In a survey of 500 students of a college, it was found that 49% liked watching football,
53% liked watching hockey and 62% liked watching basketball. Also, 27% liked
watching football and hockey both, 29% liked watching basketball and hockey both
and 28% liked watching football and basket ball both. 5% liked watching none of
these games.
1. How many students like watching all the three games?
2. Find the ratio of number of students who like watching only football to those
who like watching only hockey.
3. Find the number of students who like watching only one of the three given
games.
4. Find the number of students who like watching at least two of the given
games.

SET B-
Applicants for the doctoral programmes of Ambi Institute of Engineering (AIE) and
Bambi Institute of Engineering (BIE) have to appear for a Common Entrance Test
(CET). The test has three sections: Physics (P), Chemistry (C), and Maths (M). Among
those appearing for CET, those at or above the 80th percentile in at least two
sections, and at or above the 90th percentile overall, are selected for Advanced
Entrance Test (AET) conducted by AIE. AET is used by AIE for final selection. For the
200 candidates who are at or above the 90th percentile overall based on CET, the
following are known about their performance in CET:
1. No one is below the 80th percentile in all 3 sections.
2. 150 are at or above the 80th percentile in exactly two sections.
3. The number of candidates at or above the 80th percentile only in P is the same as
the number of candidates at or above the 80th percentile only in C. The same is the
number of candidates at or above the 80th percentile only in M.
4. Number of candidates below 80th percentile in P: Number of candidates below
80th percentile in C: Number of candidates below 80th percentile in M = 4:2:1.
BIE uses a different process for selection. If any candidate is appearing in the AET by
AIE, BIE considers their AET score for final selection provided the candidate is at or
above the 80th percentile in P. Any other candidate at or above the 80th percentile
in P in CET, but who is not eligible for the AET, is required to appear in a separate test
to be conducted by BIE for being considered for final selection. Altogether, there are
400 candidates this year who are at or above the 80th percentile in P.

5. What best can be concluded about the number of candidates sitting for the
separate test for BIE who were at or above the 90th percentile overall in CET?
 6. If the number of candidates who are at or above the 90th percentile overall
and also at or above the 80th percentile in all three sections in CET is actually
a multiple of 5, what is the number of candidates who are at or above the 90th
percentile overall and at or above the 80th percentile in both P and M in CET?
7. If the number of candidates who are at or above the 90th percentile overall
and also at or above the 80th percentile in all three sections in CET is actually
a multiple of 5, then how many candidates were shortlisted for the AET for
AIE?
8. If the number of candidates who are at or above the 90th percentile overall
and also are at or above the 80th percentile in P in CET, is more than 100, how
many candidates had to sit for the separate test for BIE?

Answer Key
1 2 3 4 5 6 7 8

75 3:4 205 270 3 or 60 170 299

10
Sequence and Series
1. The sum of the integers lying between 1 and 100 (both inclusive) and divisible
by 3 or 5 or 7 is

2.
3. The first two terms of a geometric progression add up to 12. The sum of the
third and the fourth terms is 48. If the terms of the geometric progression are
alternately positive and negative, then the first term is
4. Let both the series a1, A2, A3... and 61, 62, 63... be in arithmetic progression such
that the common differences of both the series are prime numbers. If a5 = 6g,
019 = 619 and b2 = 0, then a11 equals

5.
6. A lab experiment measures the number of organisms at 8 am every day.
Starting with 2 organisms on the first day, the number of organisms on any
day is equal to 3 more than twice the number on the previous day. If the
number of organisms on the nth day exceeds one million, then the lowest
possible value of n is
7. The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9),... and
so on. Then, the sum of the numbers in the 15th group is equal to
8. The sum of some terms of a GP is 315. Its first term is 5 and the common ratio
is 2. Find the number of its terms and the last term.
9. Sum of first 12 terms of a GP is equal to the sum of the first 14 terms in the
same GP. Sum of the first 17 terms is 92, what is the third term in the GP?
10. Consider a, b, c in a G.P. such that |a + b + c| = 15. The median of these three
terms is a, and b = 10. If a > c, what is the product of the first 4 terms of this
G.P.?

Answer Key
1 2 3 4 5 6 7 8 9 10

2838 3 –12 79 14900 -19 6119 160 92 40000

Miscellaneous
1. What is the last non-zero digit of 8218 * 15109 ?

2. In a certain city, the population grows exponentially. The population in year n

is given by the formula: Pn = 6n + 8n
Determine the remainder when the population in year 83 is divided by 49.

3. If the product of the number of medals won by three countries in the

Olympics is 2001, what is the largest possible value of the sum of the number
of medals won by them?

4. In a distant kingdom, there was a grand wizard named Mathius who guarded
a secret scroll. This scroll contained the recipe for an elixir of infinite wisdom.
The scroll was protected by an ancient magical lock that could only be opened
by solving a complex numerical puzzle. The puzzle read: "Find the number of
possible values for the natural number n such that 250 is a factor of n! but n! is
not a multiple of 340. "

5. In a fantastical realm, there is a mystical number x that holds special

properties: it leaves remainders of 2 when divided by 3, 3 when divided by 4,
and 4 when divided by 5. What is the second smallest positive integer x that
possesses these magical qualities?

6. Let X = No. of 6-digit numbers divisible by either 10, 15 or 25

Let Y = No. of 6-digit numbers divisible by 10, 15 and 25.
What will be the value of X + Y ?

7. In Round 1 of an archery match between Nam Su-hyeon and Lim Su-hyeon,

Nam scored n points and Lim scored m points, where n<m. In the second
round, Nam Su-hyeon's score decreased by 20 points, while Lim Su-hyeon's
score increased by 23 points. Surprisingly, the product of their scores from
Round 1 is equal to the product of their scores from Round 2. Determine the
minimum possible sum of their scores in Round 1

8. In a math competition set in a futuristic world, participants are challenged

with a unique problem. They need to find the 104th number in a special
sequence where a number is considered "good" if it is neither divisible by 3 nor
ends with the digit 3. With the sequence starting as {1, 2, 4, 5, 7, 8, 10, 11, 14, 16,
…}, what is the 104th term of this intriguing series that the competitors must
uncover?
9. In a fantasy world, there are three magic stones, each with a distinct power
level represented by the integers p, q, and r. These stones are used to solve two
riddles inscribed on an ancient tablet:
- The combined power of the first stone squared and the second stone,
diminished by the third stone's power, equals 100.
p2 + q - r = 100
- The power of the first stone plus the square of the second stone,
diminished by the third stone's power, equals 124.
p + q2 - r = 124

Find p+q+r.

10. Count the pairs (A, B) such that A <= B and the conditions on their Highest
Common Factor (HCF) and Lowest Common Multiple (LCM) are met, follow
these specific criteria: The HCF of and must be between 10 and 15, inclusive
and the LCM of and must be between 15 and 20, inclusive.

Answer Key
1 2 3 4 5 6 7 8 9 10

6 35 671 27 119 138000 321 172 82 2

Additional Books or Website Recommendations:

1. NSET Prep Series- here.

2. NSET Bootcamp- here.
3. Mathematics Question Bank- here.
4. Past Year Question Bank- here.
5. Arun Sharma- here.